The mechanical work required for / applied
during rotation is the torque times the rotation angle. The
instantaneous power of an angularly accelerating body
is the torque times the angular frequency.

Note the close relationship between the results for linear (or
translational) and rotational motion; the formula for the

In the rotating system, the moment of inertia, I, takes
the role of the mass, m, and the angular
velocity, ω, takes the role of the
linear velocity, v. The rotational energy of a rollingcylinder varies from one half of
the translational energy (if it is massive) to the same as the
translational energy (if it is hollow).

As an example, let us calculate the rotational kinetic energy of
the Earth. As the Earth has a period of about 23.93 hours, it has
an angular velocity of 7.29×10−5 rad·s−1. The
Earth has a moment of inertia, I = 8.04×1037
kg·m2[1]. Therefore, it
has a rotational kinetic energy of 2.14×1029 J.

Part of it can be tapped using tidal power. This creates additional
friction of the two global tidal waves, infinitesimally slowing
down Earth's angular velocity ω. Due to conservation
of angular
momentum this process transfers angular momentum to the Moon's orbital motion, increasing its distance from
Earth and its orbital period (see tidal locking for a more detailed
explanation of this process).